# Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

Given:

taking LCM m2x+ n2 = mn – 2mnx

On cross multiplying

m2x+ 2mnx + n2 – mn = 0

Comparing with standard quadratic equation ax2 + bx + c = 0

a = m2, b = 2mn, c = n2 – mn

Discriminant D = b2 – 4ac

= (2mn)2 – 4.m2. (n2 – mn)

= 4m2n2 – 4m2n2 + 4m3n > 0

Hence the roots of equation are real.

Roots α and β are given by

Hence the roots of equation are

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